Magnetic resonance microscopy determined velocity and hematocrit distributions in a Couette viscometer

Magnetic resonance microscopy is used to non-invasively measure the radial velocity distribution in Couette flow of erythrocyte suspensions of varying aggregation behavior at a nominal shear rate of 2.20 s(-1) in a 1 mm gap. Suspensions of red blood cells in albumin-saline, plasma and 1.48% Dextran added plasma at average hematocrits near 0.40 are studied, providing a range of aggregation ability. The spatial distribution of the red blood cell volume fraction, hematocrit, is calculated from the velocity distribution. The hematocrit profiles provide direct measure of the thickness of the aggregation and shear rate dependent red blood cell depletion at the Couette surfaces. At the nominal shear rate studied hematocrit distributions for the red blood cells in plasma show a depletion zone near the inner Couette wall but not the outer wall. The red blood cells in plasma with Dextran show cell depletion regions of approximately 100 mum at both the inner and outer Couette surfaces, with greater depletion at the inner wall, but approach the normal blood hematocrit distribution with a doubling of shear rate due to decreased aggregation. The material response of the blood is spatially dependent with the shear rate and the hematocrit distribution non-uniform across the gap.     

Effect of hematocrit on wall shear rate in oscillatory flow: do the elastic properties of blood play a role?

Porcine blood was used to examine the relationship between hematocrit levels and wall shear rate patterns in straight and curved artery models under fixed oscillatory flow conditions characteristic of larger arteries. It is demonstrated that porcine blood models both the viscous and elastic components of the 2 Hz complex viscosity of human blood quite accurately over a broad range of shear rates (1-1000 s-1) and hematocrits (20%-80%). For a fixed oscillatory flow waveform (Poiseuille peak shear rate = 168 s-1; mean shear rate 84 s-1), increases in hematocrit produced a decrease in the peak wall shear rate in both the straight and curved artery models and a corresponding decrease in wall shear rate reversal on the inside wall of the curved artery model. The same trends were also observed for oscillatory flows of aqueous glycerin solutions of increasing viscosity in the range of viscosity of the blood samples tested. Aqueous glycerin solutions produced wall shear rate waveforms of the same magnitude and shape as the porcine blood. This indicates that variations in the shear rate, and therefore the shear stress, were caused primarily by changes in the viscous and not the elastic properties of blood. The results suggest that simple Newtonian fluids may be sufficient for in vitro determination of the first order effects to be expected of human blood flow in large vessels having complex geometries and shear rates in or above the range of the present study.     

Blood viscosity in arctic fishes

The blood viscosity of arctic char, Salvelinus alpinus, and shorthorn sculpin, Myoxocephalus scorpius, from the arctic (74 degrees 42'N) was measured with a cone-plate viscometer. Blood viscosity of the two arctic species was considerably lower, less shear rate dependent, and less temperature dependent than the blood of winter flounder (Pseudopleuronectes americanus) from more temperate waters. The rheological properties of the arctic fish blood would minimize blood flow resistance and thus be advantageous at the low temperatures (0 degree C) characterizing their environment.     

Blood viscosity in phocid seals: possible adaptations to diving

1. Mean corpuscular volume (MCV) and mean corpuscular hemoglobin concentration (MCHC) of phocid seal red blood cells (RBC) are elevated compared to those of most terrestrial mammalian species. The influence of these characteristics on blood flow was revealed by viscosity (VIS) measurements. 2. RBC morphology and VIS of whole blood from 7 harbor seals and 5 northern elephant seals were compared with blood of the domestic pig. Samples were analysed for RBC count, white blood cell (WBC) count, total plasma proteins, hematocrit (HCT), MCV and MCHC. Viscosity measurements were made at shear rates from 11.5 to 230.4 s-1 on a Wells-Brookfield cone-plate viscometer at 37 degrees C. 3. Mean values for HCT (%), MCV (micron 3) and MCHC (%) were, respectively: elephant seal: 57, 176, 44; harbour seal: 53, 105, 38; domestic pig: 28, 54, 34. Pig blood was reconstituted to match seal blood HCTs. VIS determinations showed that seal and pig blood conform to the general mammalian dependence of VIS upon shear rate and HCT. 4. Seal blood VIS was 28% (harbour seal) and 16% (elephant seal) less than pig blood VIS at low shear (P less than 0.05). Seal blood carried more hemoglobin per unit volume than did pig blood reconstituted to the same HCT. Fewer, larger RBC with higher MCHC, and hence elevated oxygen storage, accompanied by reduced VIS and reduced flow resistance near stasis suggests that this feature of phocid seal blood is an adaptation to circulatory redistribution during long dives.     

Model-independent relationships between hematocrit,blood viscosity,and yield stress derived from Couette viscometry data

This paper describes a procedure, based on Tikhonov regularization, for obtaining the shear rate function or equivalently the viscosity function of blood from Couette viscometry data. For data sets that include points where the sample in the annulus is partially sheared the yield stress of blood will also be obtained. For data sets that do not contain partially sheared points, provided the shear stress is sufficiently low, a different method of estimating the yield stress is proposed. Both the shear rate function and yield stress obtained in this investigation are independent of any rheological model of blood. This procedure is applied to a large set of Couette viscometer data taken from the literature. Results in the form of shear rate and viscosity functions and yield stress are presented for a wide range of hematocrits and are compared against those reported by the originators of the data and against independently measured shear properties of blood.     

Hemorheology and oxygen transport in vertebrates. A role in thermoregulation?

We studied the effect of temperature on blood rheology in three vertebrate species with different thermoregulation and erythrocyte characteristics. Higher fibrinogen proportion to total plasma protein was found in turtles (20%) than in pigeons (5.6%) and rats (4.2%). Higher plasma viscosity at room temperature than at homeotherm body temperature was observed in rats (1.69 mPa x s at 20 degrees C vs. 1.33 mPa x s at 37 degrees C), pigeons (3.40 mPa x s at 20 degrees C vs. 1.75 mPa x s at 40 degrees C), and turtles (1.74 mPa x s at 20 degrees C vs. 1.32 mPa x s at 37 degrees C). This fact allow us to hypothesize that thermal changes in protein structure may account for an adjustment of the plasma viscosity. Blood viscosity was dependent on shear rate, temperature and hematocrit in the three species. A different behaviour in apparent and relative viscosities between rat and pigeon at environmental temperature was found. Moreover, the blood oxygen transport capacity seems more affected by a reduction of temperature in rats than in pigeons. Both findings indicate a greater influence of temperature on mammalian erythrocyte than on nucleated red cells, possibly as a consequence of differences in thermal sensitivity and mechanical stability between them. A comparison between the three species revealed that apparent blood viscosity measured at homeotherm physiological temperature was linearly related to the hematocrit level of each species. However, when measured at environmental temperature, rat blood showed a higher apparent viscosity than those found in species with non-nucleated red cells, thus indicating a higher impact of temperature decrease on blood viscosity in mammals. This suggest that regional hypothermia caused by cold exposure may affect mammalian blood rheological behaviour in a higher extent than in other vertebrate species having nucleated red cells and, consequently, influencing circulatory function and oxygen transport.     

On the low viscosity blood of two cold water,marine sculpins

Summary The viscosities of blood from shorthorn sculpin (Myoxocephalus scorpius), longhorn sculpin (Myoxocephalus octodecemspinosus) and winter flounder (Pseudopleuronectes americanus) were compared using a cone-plate viscometer. Both species of sculpin were almost identical with respect to blood and plasma viscosity at the temperatures (0 and 15°C) and shear rates (2.3–90/s) examined. In contrast, the viscosities of winter flounder blood and plasma were considerably greater than those observed in the sculpins. This difference in blood viscosity between the shorthorn sculpin and the winter flounder persisted over the hematocrit range of 0 to 40% red blood cells. The viscosity of the plasma and the interactions between plasma proteins and red blood cells appeared to be the major reasons for the relatively high viscosity of the flounder blood. Although a proportion of the flounder blood viscosity was attributable to fibrinogen, other plasma proteins also appeared to play a significant role. The relatively low blood viscosity of the sculpin species may confer a circulatory advantage during periods of low water temperatures.     

Rheology of embryonic avian blood

Shear stress, a mechanical force created by blood flow, is known to affect the developing cardiovascular system. Shear stress is a function of both shear rate and viscosity. While established techniques for measuring shear rate in embryos have been developed, the viscosity of embryonic blood has never been known but always assumed to be like adult blood. Blood is a non-Newtonian fluid, where the relationship between shear rate and shear stress is nonlinear. In this work, we analyzed the non-Newtonian behavior of embryonic chicken blood using a microviscometer and present the apparent viscosity at different hematocrits, different shear rates, and at different stages during development from 4 days (Hamburger-Hamilton stage 22) to 8 days (about Hamburger-Hamilton stage 34) of incubation. We chose the chicken embryo since it has become a common animal model for studying hemodynamics in the developing cardiovascular system. We found that the hematocrit increases with the stage of development. The viscosity of embryonic avian blood in all developmental stages studied was shear rate dependent and behaved in a non-Newtonian manner similar to that of adult blood. The range of shear rates and hematocrits at which non-Newtonian behavior was observed is, however, outside the physiological range for the larger vessels of the embryo. Under low shear stress conditions, the spherical nucleated blood cells that make up embryonic blood formed into small aggregates of cells. We found that the apparent blood viscosity decreases at a given hematocrit during embryonic development, not due to changes in protein composition of the plasma but possibly due to the changes in cellular composition of embryonic blood. This decrease in apparent viscosity was only visible at high hematocrit. At physiological values of hematocrit, embryonic blood viscosity did not change significantly with the stage of development.     

Blood Flow, Slip, and Viscometry

The viscosity of blood, measured by the usual viscometers in which slip is not considered, is found to be flow dependent, varying markedly with shear rate, pressure gradient, and vessel diameter in the lower ranges of these factors. The study postulates, on grounds thought reasonable, that slip may be present in blood flow, as a function of the nature of the wall surfaces, shear stress at the wall, and relative cell volume (RCV) adjacent to the wall. It presumes that blood possesses a specific, flow-independent viscosity, and determines theoretically the viscosity indications of viscometers if blood slipped in the instruments. The study shows that if the slip function is of a certain plausible form, these viscosity indications would exhibit a flow dependence of much the same pattern as the actual indications supplied by the usual viscometers. The slip postulate permits, therefore, an interpretation of the “anomalous” flow behavior of blood, dispensing with the prevailing assumption of an ad hoc variability of its viscosity with flow factors. To the extent that viscometric data for blood may be representative of other non-newtonian fluids, the slip postulate may be applicable to these fluids.     

Elasto-thixotropic properties of bronchial mucus and polymer analogs. I. Experimental results

The non-newtonian viscous and elasto-thixotropic properties of native and lyophilized pathological bronchial mucus and of polymer solutions (3% and 6% PIB in decalin) used as mucus analogs were analyzed using a cone-plate Carri-Med rheometer and a Couette viscoelastometer that we have specifically developed for measuring the rheological properties of bronchial mucus in clinical practice. The master curves obtained for apparent viscosity under steady conditions as a function of shear rates (gamma: 2.6 X 10(-3) to 6.9 X 10(1) sec-1) were fairly similar, whatever the apparatus used. Under transient conditions, at low shear rate (gamma less than 1.4 sec-1), PIB and mucus exhibited a typical viscoelastic behavior: the shear stress increased slightly up to a steady-state value. At higher gamma, a transitory overshoot of sigma characteristic of the elastothixotropic systems appeared. Such a behavior can be interpreted as resulting from structural changes such as formation and rupture of the three-dimensional network present in bronchial mucus as in polymer solutions.     

Optimal hematocrit theory during activity in the bullfrog (Rana catesbeiana).

1. There is an exponential relationship between blood viscosity (cP) and hematocrit (%) for the bullfrog; eta = 1.81 e0.033Hct. The in vitro optimal hematocrit calculated for blood flow through tubes, from this relationship for bullfrog blood, is 30%. 2. Amphibian blood is a non-Newtonian fluid with viscosity dependent on shear rate. It has a finite yield shear stress of about 1.5 dynes cm-2. 3. Hematocrit of bullfrogs was increased from 27% (control) to 57% by isovolemic erythrocythemia (constant volume blood-doping). There was a slight increase in systolic, diastolic and venous blood pressure with elevated hematocrit. 4. Systemic arch blood flow rate was inversely related to blood viscosity for erythrocythemic bullfrogs. The decrease in systemic arch blood flow at high hematocrits was due primarily to reduced pulse volume rather than reduced heart rate. 5. Systemic arch blood flow, when standardised between individuals, was inversely related to blood viscosity; Qbl = 0.185 + 3.73 eta -1. This relationship was significantly different from that predicted by the Poiseuille-Hagen flow formula. The in vivo optimal hematocrit calculated from this relationship was 41%. 6. Optimal hematocrit theory appears to be generally applicable for Rana catesbeiana in vitro and in vivo. Most individuals had an in vivo optimal hematocrit, but the absence of a clear optimal hematocrit for some individuals could reflect methodological variability, or in vivo physiological compensation for the increased blood viscosity at high hematocrit.     

Effects of cellular morphology on the viscoelastic behavior of high hematocrit RBC suspensions

Using a constant-amplitude (+/- 1 degree) oscillatory Couette viscometer (f = 0.01-1.0 Hz), we have measured the viscous (eta') and elastic (eta") components of the complex viscosity at 25 degrees C for shape-transformed human RBC suspended in isotonic buffer at 80% hematocrit. Morphology-altering drugs employed were: ECHINOCYTIC AGENT 2,4-dinitrophenol (DNP, 0.1-5 mM); STOMATOCYTIC AGENT chlorpromazine hydrochloride (CPZ, 0.01-0.1 mM). All suspensions exhibited decreasing eta' and eta" with increasing frequency. Compared to biconcave, control RBC suspensions, salient effects of shape transformation included: 1) for DNP, a dose-related elevation of both eta' and eta", with a 850% increase in eta' and a 2500% increase in eta" at 5 mM and the lowest frequency; 2) for CPZ, a dose-related elevation of both eta' and eta", with a 170% increase in eta' and a 280% increase in eta" at 0.1 mM and the lowest frequency; 3) for both DNP and CPZ, the elevations of eta' and eta" were inversely related to frequency. Using 2 mM DNP and various concentrations of CPZ, both eta' and eta" could be returned to control with 0.08 mM CPZ; further increases of CPZ at constant DNP led to elevations of both components. Comparisons of eta' and eta" to steady shear viscometric data indicated that neither a nominal shear rate approach nor a RMS complex viscosity technique was able to completely reconcile these data; a modified Kelvin-Voigt model proved useful in evaluating cellular versus membrane contributions to eta". These results indicate that RBC morphology is an important determinant of the oscillatory behavior of RBC suspensions and suggest the usefulness of the technique for studies of drug-membrane interactions.     

Measurement of blood viscosity using mass-detecting sensor

A newly designed mass-detecting capillary viscometer is extended to measure the viscosity of whole blood over a range of shear rates without the use of anticoagulants in a clinical setting. In the present study as proof of principle, a single measurement of liquid-mass variation with time replaces the flow rate and pressure drop measurements that are usually required for the operation of a capillary tube viscometer. Using a load cell and capillary, we measured the change of mass flowing through capillary tube with respect to the time, m(t), from which viscosity and shear rate were mathematically calculated. For water and adulterated bloods, excellent agreement was found between the results from the mass-detecting capillary viscometer and those from a commercially available rotating viscometer. Also, the mass-detecting capillary viscometer measured the viscosity of unadulterated whole blood without heparin or EDTA. This new method overcomes the drawbacks of conventional viscometers in the measurement of the whole blood viscosity. First, the mass-detecting capillary viscometer can accurately and consistently measure the unadulterated blood viscosity over a range of shear rates in less than 2 min without any anticoagulants. Second, this design provides simplicity (i.e. ease of operation, no moving parts, and disposable) and low cost.     

Hematorheology during deep hypothermia.

Hematologic and rheologic changes related to pure surface hypothermia procedures and procedures combining surface cooling and perfusion rewarming were studied in 16 dogs. White blood cell (WBC) and platelet counts decreased with surface cooling to about 20% of control and returned to control following surface rewarming. WBC and platelet counts returned to 80 and 50% of control depending on whether perfusion rewarming was stopped at 30 or 35 °C, respectively. Hemoconcentration was avoided during cooling with low molecular weight dextran hemodilution that was also in part responsible for a 33% decline in plasma proteins. Blood cooled in vitro and in vivo was studied by cone-plate viscometry and the viscosity noted to increase significantly as a function of decreased temperature. Computer analysis revealed that variations in temperature accounted for 75% of the variations in viscosity and variations in hematocrit contributed only 8%. An empiric formula was constructed that employs preoperative hematocrit and projected temperature to predict viscosity changes during cooling. The clinical relevance of hematologic and rheologic alterations during surface and combined hypothermia procedures was discussed.     

Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium

Single human red cells were suspended in media with viscosities ranging from 12.9 to 109 mPa s and subjected to shear flow ranging from 1/s to 290/s in a rheoscope. This is a transparent cone-plate chamber adapted to a microscope. The motion of the membrane around red cells oriented in a steady-state fashion in the shear field (tank-tread motion) was videotaped. The projected length and width of the cells as well as the frequency of tank-tread motion were measured. One-thousand eight-hundred seventy-three cells of three blood donors were evaluated. The frequency increased with the mean shear rate in an almost linear fashion. The slope of this dependence increased weakly with the viscosity of the suspending medium. No correlation was found between the frequency and four morphological red cell parameters: the projected length and width of the cells as well as the ratio and the square root of the product of these quantities. The energy dissipation within the red cell membrane was estimated based on the measured parameters and compared to the energy dissipation in the undisturbed shear flow. At constant mean shear rate the rise of the energy dissipation with viscosity is slower whereas at constant viscosity the rise with the shear rate is steeper than in the undisturbed shear flow. A fit of the data collected in this work to a theoretical red cell model might allow one to determine intrinsic mechanical constants in the low deformation regime.     

Oscillating viscometer--evaluation of a new bedside test

A viscometer for bedside blood measurements was developed, consisting of an oscillating resonator probe mounted directly into a disposable vacutainer tube for blood withdrawal. It was tested in vitro on blood samples with variable hematocrits (20-60%), increasing fibrinogen concentrations (0-20 g/l), increasing concentrations of an admixed radiographic contrast medium and erythrocyte suspensions in dextran 40 and dextran 70. Results were compared with those obtained with a conventional Couette viscometer. Oscillating viscometry yielded generally higher values than Couette viscometry, and had a good sensitivity for changes in hematocrit with a good correlation between the two methods (r=0.96, p<0.0001). Oscillating viscosity depended on the resonator frequency, it was higher at 3900 Hz than at 215 Hz, suggesting a viscoelastic behavior of blood. Erythrocyte aggregation, induced by increasing fibrinogen concentrations or dextran 70, affected oscillating viscometry. At a high frequency, i.e. a smaller penetration depth of the shear wave, oscillating viscosity tended to decrease, which suggests a depletion of the boundary layer from erythrocytes when they aggregate. At low frequency with a deeper shear wave penetration (about 50 microm), erythrocyte aggregation increased oscillating viscosity. Bedside tests in 17 patients with coronary heart disease and 10 controls confirmed the easy practicability of the test and showed lower oscillating viscosity in these patients despite higher fibrinogen concentrations presumably due to increased erythrocyte aggregation. We conclude that oscillating viscometry is an interesting bedside test, which is capable of providing new information on the biorheology of the erythrocyte-poor boundary layer near the vessel wall.     

Influence of temperature on the optimal hematocrit of the bullfrog (Rana catesbeiana)

Summary The influence of temperature on blood viscosity and consequently on the potential for oxygen transport by blood was determined using a controlled flow, variable pressure tube viscometer, and blood from adult bullfrogs. Blood viscosity was determined as a function of hematocrit and temperature, and oxygen capacity was determined as a function of hematocrit. These data were used to describe 1) the potential for oxygen transport in the tube viscometer, and 2) the relation between the optimal hematocrit, the hematocrit which provided the greates oxygen transport, and temperature. The optimal hematocrit increased at a rate of 0.237% per °C increase in temperature. This value is close to the rate of change inin vivo hematocrit of 0.246 and 0.240% per °C increase in body temperature (T_b) observed in winter bullforgs acclimated to 5 and 20°C, respectively. During the summer the hematocrit ratio showed no consistent relation to T_b. These results suggest that in bullfrogs the cardiovascular adjustments to change in T_b involve the optimal hematocrit in winter, but not in summer.     

Blood viscosity modelling: influence of aggregate network dynamics under transient conditions

This paper reports on a theoretical examination of the hypothesis that red blood cell network characteristics influence the mechanical properties of the fluid. For this purpose a newly developed energy-rate based blood viscosity model, which incorporates network dynamics, was used to predict the transient behaviour of blood viscosity (steady-state results of this model have been reported in Biorheology 46 (2009), 487-508). The main network characteristic examined in the present work was the inter-aggregate branch size and its relationship to the evolving aggregates. Branch size was used to define a network integrity index that accounted for the strength of the developed network. For the development and validation of the model, experiments performed with an optical shearing microscope, with different step-changes in shear rate, were utilised, as well as viscosity measurements under similar flow conditions performed in a double wall Couette instrument. The experimental data were compared with the response of the model, which incorporated the network integrity index. The results suggest that network characteristics may influence the viscosity of blood at low shear rates and exhibit good agreement with experimental observations.     

Concentration-dependent, temperature-dependent non-Newtonian viscosity of lung surfactant dispersions

The bulk shear viscosities of aqueous dispersions of lavaged calf lung surfactant (LS) and its chloroform:methanol extract (CLSE) were measured as a function of concentration, shear rate and temperature. At 10-mg phospholipid per milliliter, dispersions of LS and vortexed CLSE in 0.15 M NaCl (saline) had low viscosities near 1 cp over a range of shear rates from 225 to 1125 s(-1). Lung surfactant viscosity increased with phospholipid concentration and became strongly non-Newtonian with higher values at low shear rates. At 37 degrees C and 40 mg/ml, LS and vortexed CLSE in saline had viscosities of 38 and 34 cp (77 s(-1)) and 12 and 7 cp (770 s(-1)), respectively. Viscosity values for LS and CLSE were dependent on temperature and, at fixed shear, were lower at 23 degrees C than at 37 or 10 degrees C. Hysteresis was also present in viscosity measurements depending on whether shear rate was successively increased or decreased during study. Addition of 5 mM Ca(2+) at 37 degrees C markedly reduced CLSE viscosity at all shear rates and decreased LS viscosity at low shear rates. Dispersion by sonication rather than vortexing increased the viscosity of CLSE at fixed shear, while synthetic phospholipids dispersed by either method had low, relatively Newtonian viscosities. The complex viscous behavior of dispersions of LS and CLSE in saline results from their heterogeneous aggregated microstructure of phospholipids and apoproteins. Viscosity is influenced not only by the aggregate surface area under shear, but also by phospholipid-apoprotein interactions and aggregate structure/deformability. Similar complexities likely affect the viscosities of biologically-derived exogenous surfactant preparations administered to patients in clinical surfactant therapy.     

Temperature dependence of the yield shear resultant and the plastic viscosity coefficient of erythrocyte membrane. Implications about molecular events during membrane failure.

Structural failure of the erythrocyte membrane in shear deformation occurs when the maximum shear resultant (force/length) exceeds a critical value, the yield shear resultant. When the yield shear resultant is exceeded, the membrane flows with a rate of deformation characterized by the plastic viscosity coefficient. The temperature dependence of the yield shear resultant and the plastic viscosity coefficient have been measured over the temperature range 10-40 degrees C. Over this range the yield shear resultant does not change significantly (+/- 15%), but the plastic viscosity coefficient changes exponentially from a value of 1.3 X 10(-2) surface poise (dyn s/cm) at 10 degrees C to a value of 6.2 X 10(-4) surface poise (SP) at 40 degrees C. The different temperature dependence of these two parameters is not surprising, inasmuch as they characterize different molecular events. The yield shear resultant depends on the number and strength of intermolecular connections within the membrane skeleton, whereas the plastic viscosity depends on the frictional interactions between molecular segments as they move past one another in the flowing surface. From the temperature dependence of the plastic viscosity, a temperature-viscosity coefficient, E, can be calculated: eta p = constant X exp(--E/RT). This quantity (E) is related to the probability that a molecular segment can "jump" to its next location in the flowing network. The temperature-viscosity coefficient for erythrocyte membrane above the elastic limit is calculated to be 18 kcal/mol, which is similar to coefficients for other polymeric materials.